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Factor: 5a²-4a-28

There is only one way to factor 5a², and that is 5a and a,
so we write

(5a  )(a  )

There are these ways to factor |-28| or 28 

28·1, 14·2, 7·4, 4·7, 2·14, 1·28

We start trying them, by FOILing only looking at outers and inners
to see if they have a difference of |-4a|, or 4a.
(since the sign of the last term is -.

(5a 28)(a 1)   outers = 5a, inners = 28a, difference = 23a, not 4a
(5a 14)(a 2)   outers = 10a, inners = 14a, difference = 4a.

So we didn't have to try the rest, we just need to place
the signs so that the outers and inners will have sum -4a.
14a is larger than 10a so the 14 gets - and the 2 gets +.

Answer: (5a-14)(a+2)

Edwin